This study is designed to test the hypothesis that a murine anti-B4 monoclonal antibody coupled to ricin will act as an immunotoxin by targeting and destroying cancer cells that express the B4 surface antigen and can be safely administered to patients with refractory B-cell lineage leukemia or lymphoma. The following specific aims will be addressed in this Phase I study: 1) to determine the maximum tolerable dose of anti-B4- blocked ricin given as a seven day continuous infusion, then a seven day rest followed by a second day infusion; 2) to determine the antitumor activity of anti-B4-bR in children with refractory/relapse B-lineage malignancies (leukemia and lymphoma) within the confines of a Phase I study; 3) to monitor patients on this schedule for the development of human anti-mouse antibody (HAMA) and human anti-ricin antibody (HARA); and 4) to determine the serum level of anti-B4-bR at the end of a seven day infusion.